02/17/16
1
2
3
4
5
1
ROUGH DRAFT; COMMENTS WELCOME
What We Talk About When We Talk about Causality
Jim Bogen, Center for Philosophy of Science, University of Pittsburgh (jbogen@pitt.edu)
<<13168 words>>
6
i. Until recently, the standard views about causality were driven by the Humean dogma that
7
ignoring expectations and other psychological factors, causal relations boil down to some sort of
8
regularity among actual and possible occurrences of things like the cause and things like the
9
effect. Hume himself thought that actual occurrences of things like the cause must always be
10
followed by actual occurrences of the effect under similar circumstances.(*cite) Analytically
11
minded 20th century Humeans believed causal explanations require the derivation of canonically
12
worded descriptions of the effect or the probability of its occurrence from canonical descriptions of
13
initial conditions and universally applicable, exceptionless scientific laws whose modal status
14
makes them suitable for the derivation of counterfactual claims. .(*Hempel). The apparent scarcity
15
of real world scientific causal processes which satisfy stringent regularity conditions led many
16
latter day Humeans to retreat to a more modest view. They continue to think the things physicists
17
explain are instances of laws (general relativity field equations and Schrodinger’s equation, for
18
example) which describe exceptionless regularities. But they think biologists, psychologists,
19
sociologists, and others who work in special sciences must somehow make do with contingent,
20
second rate generalizations which hold locally rather than universally, are prone to exceptions,
21
and hold only to an approximation of the systems whose effects they explain.(*cites including
22
Beatty and *Mitchell, Phil Sci,) Latter day Humeans can’t explain how such low grade principles
23
can deliver satisfactory explanations unless they can be reduced to genuine laws. Their failure to
24
provide detailed reductions leaves them with little to say about causal explanations in the special
25
science.
26
To make matters worse, there are reasons to doubt the truth and universal applicability of
27
generalizations from physics which Humeans typically consider to be genuine laws of
28
nature.(*Cartwright, Scriven, Woodward PSA 2000, etc. and *Earman (in conversation) on how
29
hard it is to think that Relativity and Quantum Mechanics laws are both correct.) Some Humeans
30
say the problematic generalizations are true ceteris paribus. This collapses into the triviality that
31
explanatory laws are true whenever they are true unless the ceteris conditions can be specified in
32
some detail. But when they are spelled out, the things the laws are supposed to explain often
33
turn out to occur under circumstances which fail to satisfy them. When this happens, It is hard to
34
see why the truth of the ceteris paribus laws should make any difference to the goodness of an
35
explanation. Humeans tend to think we want an explanations for things which puzzle us because
36
we didn’t expect it to happen. If so, it should satisfy our desire for an explanation to show that an
37
effect is an instance of a regularity..(*Cite Hempel) But then ceteris paribus laws can’t explain
02/17/16
1
effects which occur in situation which fail to satisfy the ceteris paribus conditions.(*Cite
2
Cartwright)1
3
2
So many difficulties have plagued the Humean program that it would be perverse not to look for
4
a happier account of causal explanation The most promising alternatives to Humeanism are
5
Mechanism (as developed by various permutations of Machamer, Darden, and Craver), and
6
systematic dependence accounts of causality (SD) like Jim Woodward's.(*cite) Both reject the
7
Humean idea that causal explanations depend on laws as traditionally understood.
8
SD maintains a variant of the traditional idea that regularity is crucial to causality, but the
9
regularities it believes to be characteristic of causal processes differ from those of standard
10
Humean accounts. For one thing, they are counterfactual regularities which obtain among ideal
11
interventions on factors belonging to the system which produces the effect to be explained, and
12
the results which would ensue if the interventions occurred. Furthermore, because the required
13
regularities typically hold only for some interventions, the generalizations which describe them
14
need not qualify as genuine Humean laws. Mechanism is an even more drastic departure from
15
Humeanism. It maintains that a causal explanation must describe the system which produces the
16
effect of interest by enumerating its components and what they do to contribute to the production
17
of the effect. Mechanists acknowledge that some mechanisms operate with great regularity, but
18
they do not believe that the understanding we get from a causal explanation derives from its
19
description of actual or counterfactual regularities.
20
Our view is that the Humean program has broken down, and that Mechanism offers a better
21
account of causal explanation than SD. After sketching these two accounts in a little more detail
22
(§ii below) we look (in §iii) at some typical neuroscientific explanations. They are of interest first,
23
because they actually do appeal to some highly general principles (Nernst’s equation, Ohm’s law,
24
the Goldman, Hodgkin, Katz Constant Field equation and the Mullins and Noda Steady State
25
equation) which look, as much as anything in this area of neuroscience, like Humean laws. But
26
as we’ll see, they, and the uses to which they are put, are decidedly and illuminatingly non-
27
Humean. Secondly, the explanations we consider involve a number of somewhat more limited
28
generalizations about what goes on, or what can be expected to go on in the neuron under
29
specified conditions. SD and Mechanism can be expected to tell significantly different stories
30
about such generalizations. We use them (in § iv) to highlight some important differences
31
between these alternatives to Humeanism. Finally, we set out some of our reasons for preferring
32
Mechanism (§*) and conclude with some general remarks about activities.
33
ii. According to Machamer, Darden, and Craver (MDC), causal mechanisms consist of
1
Davidson tried to finesse the scarcity of explanatory principles which qualify as laws by
suggesting that you can be right to claim that X causes Y even if you don’t know what laws cover
them as long as there are laws to be found.(*cite) But as with the idea that natural laws are true
because they include ceteris paribus clauses, it is hard to see the point of Davidson’s suggestion
02/17/16
1
2
3
3
…entities and activities organized such that they are productive of…changes
from start or set-up to finish or termination conditions.(MDC, p.3) 2.
4
The finish or termination conditions are the effects explained by an account of the workings of the
5
mechanisms which produce them. For example, the electro-chemical mechanism by which the
6
signal is transmitted includes such entities as cell membranes, vesicles, microtubules, molecules
7
and ions. The startup conditions include ‘the relevant entities and their properties’ along with
8
‘various enabling conditions…such as the available energy, pH, and electrical charge
9
distributions…’ including the relevant features and states of the neurons and some of the items in
10
their immediate environment. (MDC, p.8, 11) Ions repelling ions of similar charge, proteins
11
bending into configurations involved in the passage of sodium ions through channels in the cell
12
membrane, and the movements of these and other ions are among the activities by which the
13
entities which belong to the mechanism contribute to the transmission of a neuronal signal.
14
Reliable mechanisms (the neural signal transmission mechanism is an example) operate
15
uniformly under normal conditions to produce their effects with a high degree of regularity. An
16
adequate account of a reliable mechanism and the conditions under which it operates should
17
therefore enable us to understand the regularities exhibited by the workings of its parts, to predict
18
what effects the mechanism will produce or fail to produce under specified conditions, and to
19
retrodict facts about the mechanism from results it has already produced. It should also enable
20
us to predict the effects of changes in the mechanism or the conditions under which it operates. 3
21
But not all effects are produced by reliable mechanisms. Satisfactory mechanistic explanations
22
can sometimes be given for effects resulting from mechanisms whose operations are too irregular
23
to enable us to reliably predict their future performance, or to systematically explain why they
24
sometimes fail to produce the effects they produce on other occasions. For example, you can
25
explain what gets a chain saw started even if it’s an old chain saw that starts infrequently and
26
irregularly. Thus Mechanists do not believe that actual or counterfactual regularities are
27
necessary for the explanation of an effect. Even for an effect produced by a highly reliable
28
mechanism, to provide an explanation which renders the effect intelligible is to show how it is
29
produced by entities and their activities rather than to describe the regularities instanced by its
30
production, or to break them down into more elementary regularities exhibited by the operation of
if explanations are supposed to show us that the effects they explain were to have been
expected.
2 The original passage says the activities and entities produce regular changes from start up to
finish conditions. We deleted ‘regular’ to avoid the suggestion that all mechanisms operate
reliably to produce their effects with great regularity.
3 MDC claimed that the regularities exhibited by reliable mechanisms ‘support
counterfactuals’.(MDC pp.7-8) This claim requires qualifications for reasons we take up in §vi
below.
02/17/16
4
4
1
parts of the mechanism.(MDC p.22)
2
explanations, Mechanism must provide an alternative to Humean and SD accounts of the roles
3
they play.
4
Accordingly, when generalizations do figure in
SD agrees with Mechanism that causal explanations make things understandable by describing
5
the influences of causal factors, rather than by subsuming explananda under laws. But SD and
6
Mechanism have different understandings of the difference between a causally productive
7
relation between the values of two things (events, etc.) X and Y, and a correlation which is
8
coincidental, or due to a common cause rather than X’s causal influence on the value of Y. (Here
9
and throughout this paper we use the term ‘value’ broadly for qualitative as well as qualitative
10
states, features, conditions, of a thing as well as for it’s presence or absence at a given time or
11
place.) According to Woodward the difference turns on whether there is an invariant
12
counterfactual relation between changes in the value of Y and at least some ‘interventions on X
13
with respect to Y’(*cite) For example, suppose values of X are amounts of diphtheria toxin in a
14
patient’s throat, and values of Y are levels of inflammation of the lining of the throat. If the toxin is
15
causally productive of (not just accidentally related to) throat inflammation, it should be
16
counterfactually the case that if ideal manipulations were performed to introduce different
17
amounts of toxin into the throat, then (at least for quantities falling within a certain range) there
18
would be an invariant relation between levels of inflammation and amounts of toxin. An
19
intervention on X with respect to Y must change the value of X without exerting any influence on
20
anything which could change the value of Y independently of the change in the value of X. This
21
disqualifies introducing the toxin by putting it on an instrument and vigorously scraping the throat
22
lining. That’s because vigorous scraping can inflame the throat independently of the toxin. It is
23
not required that the values of Y change in a regular way under all interventions on X. Thus SD
24
can allow that after the amount of toxin reaches a critical level, the throat will be incapable of
25
further inflammation, and that toxin levels below a critical amount will not produce any observable
26
inflammation. What SD requires is that values of Y change in a regular way with interventions on
27
X within a limited range. (*Cite, e.g., (Woodward long PSA 2000 p.6.) And to distinguish X
28
exerting a causal influence on Y, from Y exerting a causal influence of X, Woodward requires
29
rather that values of X should not change in a systematic way with interventions on Y with respect
30
to X.
In supposing that causal regularities don’t explain, but require explanation by appeal to the
activities of individual entities and collections of entities, the mechanist account harks back to
Aristotle’s idea of efficient causes which do their work by exercising their capacities to produce
changes in things.(*cites) It agrees with Anscombe’s idea that rather than signifying a single
productive relation which obtains between all causes and their effects, the verb, ‘cause’ is better
thought of as a place holder for specific kinds of productive activities rather than the name (cite*).
It agrees, in spirit at least with Cartwright's vision of causal explanation as turning on the
identification and measurement of natural capacities, and her objections to traditional tales of
natural laws.(cite*)
4
02/17/16
1
5
One of Woodward's own examples features the acceleration of a block sliding down an inclined
2
plane. The magnitude of the acceleration varies with a net force, F n, whose magnitude depends
3
upon N, a force perpendicular to the motion of the block due to its weight, and a frictional force,
4
Fk. At the surface of the earth, N varies in a fairly regular way with mg, the product of the block’s
5
mass (m) and the acceleration of a body in free fall at the surface of the earth (g), along with the
6
cosign of , the angle of the incline, for a limited range of values of . As long as certain features
7
of the plane and its environment stay the same (e.g., it isn’t greased or roughed up) the frictional
8
force, Fk varies in a regular way with mg cos  for a limited number of values of . Thus
1.1 Fnet = mg sin  - mg cos , and
9
10
1.2 the acceleration of the block (a) approximates to g sin  -g cos  as long as the inclined
11
plane is at the surface of the earth, and the earth maintains the same mass and radius.
12
An ideal intervention on m with respect to F net would be an operation which changes the mass of
13
the block without changing , or any of the other factors which might independently change the
14
value of the net force (e.g., without roughing up the plane, moving the inclined plane away from
15
the earth, introducing wind resistance, etc.). An ideal intervention on  with respect to Fnet would
16
be an operation which changes the angle of incline without changing anything else which might
17
independently affect the value of the net force. An intervention on  with respect to a would be an
18
operation which changes the angle of the incline without changing anything else which could
19
independently affect the acceleration of the block. Ignoring niceties, to perform an ideal
20
intervention on X (e.g., m or ) with respect to Y (e.g., Fnet, or a), one must change X in such a
21
way that nothing which could independently affect Y changes except as a result of the change in
22
X. As said, Woodward thinks it is characteristic of causal interactions that if X exerts a causal
23
influence on Y, the relation between them is ‘invariant’ for interventions on X within a limited
24
range of values of X. Equations 1.1 and 1.2 describe invariances in the relations between some
25
values of m and Fnet, between  and a, and so on. Since these equations do not hold under all
26
background conditions or for all values of  or m5 they are not Humean laws. As said, they
27
describe counterfactual regularities like those which obtain among ideal interventions which
28
change angles of incline and accelerations, masses and net forces, etc. within a certain range
29
under certain sorts of background conditions.
30
31
32
33
34
As Woodward observes, SD is meant to articulate such intuitions as that
[i]f X causes Y, one can wiggle Y by wiggling X, while when one wiggles Y, X
remains unchanged,
and
If m were increased too much, the incline would break. If is too large, the block will fall off. If
the block were immersed in water, the black would float away. The inclined plane must not be
too far away from the earth. And so on.
5
02/17/16
1
2
3
4
5
Woodward believes such intuitions are so central to our understanding of causality that
6
counterfactuals dealing with ideal interventions on X with respect to Y should be understood as
7
incorporated ‘into the content of causal claims’.(Woodward 2000 p.11)
6
[i] f X and Y are related only as effects of a common cause C, then neither
changes when one intervenes and sets the value of the other, but both can be
changed by manipulating C.( Hausman and Woodward 1999, p.533).
8
The disagreement between Mechanism and SD is made vivid by an argument of Woodward’s
9
intended to show that the difference between a non-causal interaction involving X and Y, and an
10
interaction in which X produces a change in Y, is not that ‘an interaction counts as [causally]
11
productive…as long as it involves some activity’. 6 If Alice takes birth control pills and fails to
12
become pregnant, the pills’ active ingredients engage in all sorts of activities including dissolving,
13
entering the bloodstream, forming chemical bonds, etc., regardless of whether Alice is a fertile
14
woman and the pills play a causal role in preventing her pregnancy, or Alice is Alice Cooper 7 to
15
whose non-pregnancy they are causally irrelevant. Typical birth control pills are fail safe devices
16
containing chemicals which interfere with the release of eggs from the ovary, thicken the cervical
17
mucus to hinder the movement of sperm, and render the lining of the uterus unsuitable for the
18
implantation of fertilized eggs. According to Mechanism these chemicals are causally relevant
19
when they do things which interfere with the mechanisms by which eggs are produced, sperm
20
moves through cervical mucous, and fertilized eggs are implanted in the lining of the uterus.
21
They are causally irrelevant in males because males have no egg production, uteri or cervical
22
mucous for them to interfere with. By contrast, Woodward thinks the pills are relevant to Alice’s
23
non-pregnancy if her taking the pills is an instance of the kind of intervention which is
24
counterfactually related in a regular way to the prevention of pregnancy. They are irrelevant to
25
Alice Cooper’s non-pregnancy ‘because even if…[he] had not taken them, he would have failed to
26
become pregnant.’(Woodward [2000] p.11) The Mechanist denies that the causal influence of the
27
chemicals in the pill is to be explained in terms of, or depends upon counterfactual regularities.
28
We don’t know whether Woodward believes activities are always necessary to causation, or
29
whether some things exert their causal influences by virtue of conditions, states, features, etc.,
30
which are not activities. But to the extent that the activities of chemicals in the pill are causally
31
significant, Woodward thinks their significance turns on, and is to be understood by appeal to,
32
counterfactual regularities involving ideal interventions. Woodward paraphrases Robert
33
Weinberg’s account of the difference between describing and explaining a biological process to
34
illustrate the motivation for his emphasis on counterfactual invariances among ideal interventions
35
and their results..
36
37
According to Weinberg, biology is now an explanatory [rather than a merely
descriptive] science because we have discovered theories and experimental
6
7
*note on bottom out/non bottom out activities.
We have changed Woodward’s example by identifying its hero.
02/17/16
1
2
3
4
5
6
7
8
9
7
techniques that provide information about how to intervene in and manipulate
biological systems. Earlier biological theories...fail to provide such
information, and for that reason are merely descriptive. As Weinberg puts it,
molecular biologists correctly think that “the invisible microscopic agents they
study can explain at one essential level the complexity of life’ because by
manipulating those agents it is now ‘possible to change critical elements of the
biological blueprint at will’.(‘What is a mechanism?’ p. 10).
Judging from the paraphrase, Weinberg claims (and so would we) that in order to control a real
10
system scientists need a causal theory which tells them about how to perform real world
11
manipulations on the relevant causal factors. What this suggests to Woodward is the significantly
12
different idea that philosophers need to incorporate counterfactual conditionals concerning the
13
effects of ideal interventions (recall that these are manipulations of a very special kind) into their
14
accounts of causal explanation. Mechanism grants the importance of causal knowledge to the
15
control of a real system, but it denies that counterfactuals about the results of ideal interventions
16
on X with respect to Y are part of the content of the claim that X exerts a causal influence on Y.
17
iii. We turn now to our discussion of explanations which seem to involve Humean laws and
18
descriptions of counterfactual regularities among ideal interventions and their results. Having
19
described them, we will suggest Mechanism friendly alternative construals of them.
20
The membrane potential (Vm) of a segment of neuronal membrane is the difference between
21
the electrical potential just outside and just inside of it. The membrane potential of neurons at
22
rest ranges, in different species of organisms, between –40 and –90 millivolts (mV)--the minus
23
sign indicating that the charge just inside the membrane is negative in comparison to the charge
24
just outside. Intra cellular electrical currents are generated and propagated (along an axon, for
25
example) when sites along the membrane depolarize, i.e., when Vm becomes less negative.
26
Action potentials occur when membrane depolarization reaches a critical threshold. When the
27
membrane depolarizes (when Vm becomes more negative and moves toward its resting level)
28
they cease to occur; no further action potentials are propagated until the next depolarization.
29
The facts to be explained have to do with resting state membrane potentials, and the
30
propagation of action potentials. The latter are currents which rapidly traverse the neuron without
31
modification or diminution to excite or inhibit neuronal activity on the other side of a synapse. The
32
explanations we will consider depend upon the empirically well established fact that the effects of
33
interest depend upon distributions and behaviors of charged ions, including Na+, K+ and Cl-, to be
34
found in changing concentrations just inside and just outside the cell membrane. In particular, it
35
is generally agreed that the sign and magnitude of the membrane potential depends upon the
36
cross membrane ratio of negatively to positively charged ions. The leading idea of the
37
explanations is that changes in membrane potential depend upon changes in these ratios due to
38
transmembrane and intracellular ion flows.
39
The neuronal membrane is permeable to potassium, less permeable to sodium, and still less,
40
but somewhat permeable to chlorine ions. Accordingly, these ions tend to leak at different rates
02/17/16
8
1
through the membrane down their concentration gradients; regardless of charge, they tend to
2
move from regions of higher to regions of lower concentration. They also tend to move down
3
their electrical gradients: positively charged ions tend to move from more toward less positively
4
charged locations; negative ions tend to move from more to less negatively charged locations.
5
The Nernst equation (said by one textbook to be so fundamental to our understanding of neuronal
6
signaling that ‘if you learn only one equation in your study of neurobiology, the Nernst
7
equation…is the one to learn’(Shepherd, p.91)) describes the equilibrium potential for a highly
8
idealized, imaginary cell whose membrane is permeable only to ions of a single kind. For any
9
species of ion, X, the equilibrium potential (Ex) is the membrane potential required to offset the
10
tendency of X ions to move across the membrane because of the difference between the
11
concentration of X ions just outside the membrane [X]out, and their concentration [X]in just inside.
12
The equilibrium for any ion is proportional, not to the ratio of the concentrations on either side of
13
the membrane, but to its natural log:
14
2. Nernst: EX =
RT
logn
zF
[X] out
where R is the thermodynamic gas constant, T, the absolute
[X] in
15
temperature, z, the valence of the ion, and F is the Faraday measure of the electrical charge in
16
one mole of ions of the same valence as X. If the membrane of a typical neuron was permeable
17
only to one species of ion, if it resembled in other significant respects the ideal cell the Nernst
18
equation faithfully describes, and if its resting potential was identical to the equilibrium potential
19
for the ion to which its membrane is permeable, then its membrane potential would be due just to
20
the factors which determine the ratio of extracellular to intracellular concentrations of the relevant
21
ion. But real neurons aren’t like that, and their membrane potentials differ from what they should
22
be according to the Nernst equation. Thus whatever the Nernst equation contributes to our
23
understanding of the membrane potential of a real neuron, it does not describe a regularity
24
actually instanced by the membranes of resting neurons, and its explanatory role cannot be that
25
of a Humean covering law.
26
So what good is the Nernst equation? The answer lies in the use to which it was put in studying
27
the facts which explanations of resting and other membrane potentials must take account of.
28
Discrepancies between the Nernst equilibrium potential for potassium and actual membrane
29
potentials were established experimentally by measuring changes in the magnitudes of resting
30
potentials as more and more potassium was added to the fluid outside of a neuron in an
31
experimental preparation. To account for the discrepancies, Goldman, Hodgkin, and Katz
32
proposed that membrane potentials varied with distribution of chlorine and sodium, as well as
33
potassium ions. Assuming that no ions traverse the membrane of a resting cell, and therefore
34
that the cross membrane voltage gradient is perfectly stable, the Nernst equation suggests that if
35
the membrane were equally permeable to all of these ions, the membrane potential should be
02/17/16
9
1
proportional to the log of ([K]out/[K]in + [Na]out/[Na]in + [Cl]in/[Cl]out.8 But because the permeabilities
2
differ, different electrical potentials are required to maintain equilibrium for different species of
3
ions. To take account of this, Goldman, Hodgkin, and Katz weighted the concentration ratios by
4
multiplying each one by a different permeability ratio (pK for potassium, PNa for sodium, etc.) to
5
obtain the equation
3. Constant Field Equation:9 Vm = 58 log
6
pK[K]out
pK[K]in
 pNa[Na] out  pCl[Cl]in 10
.
 pNa[Na] in  pCl[Cl]out
7
This equation tells us--for an imaginary cell in which the resting potential is an equilibrium
8
potential which varies with no factors other than K, Na, and Cl concentrations and the membrane
9
permeabilities to these ions--what the cross membrane ion concentration ratios would have to be
10
to maintain Vm at close to the value calculated from measurements of real resting potentials.
11
Notice, however, that although the Constant Field Equation is more faithful to real membrane
12
potentials than the Nernst equation, it correctly describes Vm only for imaginary cells whose cross
13
membrane voltage gradients are uniform, and whose membrane potentials vary only with the
14
factors the equation mentions. Real neurons don’t work that way either-- especially because
15
potassium and sodium leak through the membrane while the cell is at rest. Thus even though it
16
describes membrane potentials more accurately than the Nernst equation, exceptions to the
17
constant field equation are the rule rather than the exception, and so it cannot be a Humean law.
18
Mullins and Noda provided a still more accurate description by dropping the assumption that V m
19
is an equilibrium potential and taking potassium and sodium leakage into consideration. They
20
suppose that at rest, the membrane potential is maintained in a steady state by a mechanism
21
which actively moves sodium and potassium across the membrane as required to compensate for
22
the leakage due to membrane permeability . Accordingly, Mullins’ and Noda’s Steady State
23
equation weights the cross membrane ion concentration ratios by a cross membrane transport,
24
as well as permeability constants. Ignoring chlorine, their equation can be written
25
4. Vm =58 log
 b[Na] out
. Here, r is the ratio of active sodium to potassium transport
r[K] in  b[Na] in
r[K]out
26
which corrects for leakage, and b is the ratio of sodium to potassium permeability which allows
27
leakage.
28
Solutions of the Steady State Equation approximate to real resting potential magnitudes if r is
29
written 3Na out/2 K in. So written, the Steady State equation is a contingent generalization which
30
holds only on average. It does not explain the resting potential, and would not do so even if it
31
delivered even better approximations of the real quantities. Instead, by describing relations which
8
The last term is an inner to outer rather than an outer to inner ratio because chlorine ions are
negatively charged, and their electrical gradients run in a direction opposite to the electrical
gradients of sodium and potassium.
9 So called because it assumes an equilibrium such that the cross membrane electrical field is
perfectly uniform.
02/17/16
10
1
obtain between membrane potential, and transport, permeability, and concentration ratios, the
2
equation sets out facts to be explained, and places constraints on their explanation. For
3
example, according to 4., an adequate explanation of the resting potential must tell us what
4
factors account for sodium and potassium transport, how they do their work, and why they
5
operate in such a way that on average, two potassium ions enter the cell for every 3 sodium ions
6
which flow out. The standard explanations posit, and describe the structure and behavior of a
7
complex protein located in the membrane which pumps sodium out and potassium in through the
8
membrane. Various schemes have been suggested for the operation of this Na-K pump. All of
9
them propose that the pump has sites which bind and release sodium and potassium ions to
10
pump them in and out of the neuron. All of them describe the pump as operating in such a way
11
that that its sodium and binding sites are exposed in alternation
…(presumably within a channel like structure) to the extracellular and
intracellular solutions. The cyclic conformational changes are driven by
phosphorylation and dephosphorylation of the protein and are accompanied
by changes in binding affinity for the two ions. Thus sodium is bound during
intracellular exposure of the sites and subsequently released to the
extracellular solution; potassium is bound during extracellular exposure and
released to the cytoplasm.(Nicholls et al, pp. 82-3)
12
13
14
15
16
17
18
19
20
The energy the protein requires to transport the ions is provided by ATP hydrolysis.(p.81) 11
21
Contrary to the Humeans, this aspect of the resting potential is explained by describing the Na-K
22
pump and saying what its various parts do to help maintain the resting potential, rather than by
23
subsuming events under universally applicable, exceptionless, non-contingent laws.
24
The pump operates in a highly regular way. In addition to the fact that
5. ‘[a]n average of three sodium and two potassium ions are bound to the Na-K pump for
25
each molecule of ATP hydrolyzed’(Nicholls et al, p.82),
26
27
we are told, for example, that the pump’s binding affinity changes in a regular way with the
28
position of the binding sites in such a way that sodium is bound inside the membrane, and
29
released outside of it, while potassium is bound outside and released inside the membrane.
30
Conforming as it does to limited regularities like these the pump contributes to the maintenance of
31
the resting potential in accordance with the Steady State equation, and to lessor degrees, with
32
the Constant Field and Nernst equations. Generalizations like 5. set out details an adequate
33
explanation must account for. In so doing, they like, the Nernst, Steady State, and Field
34
equations constrain explanations and help guide investigations. Finally, the regularities they
35
describe are also significant because as long as they obtain, the Na-K pump will operate in the
36
same way, and its components will behave in the same ways to make the same contributions to
10
58 log is the value of RT/zF multiplied by 2.306 to convert the log to base 10.
cp. Alberts et al, pp.209ff., 512—527,Levitan and Kaczmarek, pp 114-115, Shepherd, pp.7477, Kandel, et al, pp.86ff.
11
02/17/16
11
1
the resting potential. As long as this continues to be the case the same explanation will account
2
adequately for the facts of interest about the resting potential.
3
Without going into the details we have no space for, roughly the same thing can be said about
4
the explanation of the action potential. Recall that at rest, the charge just inside a neuron’s
5
membrane is negative relative to the change just outside the membrane. Hodgkin and Katz
6
found that when they increased the concentration of sodium outside of the membrane, enough
7
sodium flowed in to depolarize it, and that an action potential developed when the depolarization
8
reached a certain level. They found also that at the peak of the action potential, the membrane
9
potential varies with the extracellular sodium concentration. Using the Constant Field equation,
10
they calculated that the measured variation in the membrane potential is roughly what it should
11
be if the membrane becomes more permeable to sodium by a factor or roughly 500. This
12
application of the Constant Field equation does not tell us what causes the action potential, any
13
more than the bullets in a murder victim’s body tell detectives who murdered her. Instead, just as
14
the detectives can apply ballistics methods to the bullets to find out what kind of gun the murderer
15
used,, the investigators used the Constant Field equation to figure out that the action potential
16
was initiated by a causal influence which increased the membrane’s sodium permeability. And
17
the equation constrained the explanation of the action potential by indicating how great a change
18
in sodium permeability an adequate explanation would have to account for. (*Nicholls et al p.91)
19
The detectives learn they should look for a suspect who possessed a certain kind of gun, the
20
investigators learned that they should look for a sodium channel which opens with depolarization.
21
Action potentials can be initiated experimentally by artificially depolarizing a very small stretch
22
of membrane to produce a sodium influx which produces an electrical current just inside the
23
depolarized membrane. But what maintains the current at the same level as it traverses the
24
axon? Why isn’t it diminished, by sodium leakage, interference from transient local currents, and
25
so on? It was found that a bit of membrane a little further down the axon is depolarized to
26
threshold level by sodium ions moved downstream by mutual electrical repulsion from the place
27
they entered. When this happens, more sodium flows into the cell through the newly depolarized
28
membrane. When a bit of membrane downstream from there reaches threshold depolarization, a
29
new sodium influx occurs. And so on. This enables the current to travel down the neuron in the
30
form of a wave without loss of amplitude. The sodium influxes involved in this process are
31
explained as due to operation of a series of voltage gated sodium channels. The channel is
32
thought to be a protein structure with components which can shift back and forth under the
33
influence of changes in membrane potential between a configuration which decreases, and a
34
configuration which increases sodium permeability. 12 A complete explanation would include a
12
For details see Kandell et al 111-134..
02/17/16
12
1
detailed account of the molecular structure and the operation of this gate. 13 One of the things the
2
account would have to tell us is why the channel opens with depolarization and closes with
3
hyperpolarization. Investigators have begun to describe the structure of the protein which
4
constitutes the channel, and have proposed a model for the configurations and configuration
5
shifts of the positively charged components involved in permeability changes. One of the facts
6
they must take account of is that the process is stochastic; threshold membrane depolarization
7
greatly raises the probability that a channel will open, but does not deterministically guarantee
8
that it will. (Nichols et al. p.31,93).
Our final example is Ohm’s law which says that I(current flow between two points)
9
10
=V(voltage)/R(resistance). It is used to describe the electrical current in an ideal circuit used to
11
model features of the electrical activity in a neuron. The current due to the flow of ions of any
12
given species, X, (iX) varies with a driving potential equal to Vm-EK (the difference between the
13
membrane potential and the ion’s equilibrium potential) and conductance, gX. gX is the reciprocal
14
of resistance. The magnitude of gX varies with, but is not identical to membrane permeability to
15
the ion. Thus for sodium, Ohm’s law can be rewritten as iNa = gNa (Vm – ENa), and the current due
16
to the flow of ions of more than one kind can be calculated from their conductances and driving
17
potentials.(Levitan and Kaczmarek p.94) Like Nernst’s equation, the Constant Field equation,
18
and the Steady State equation, Ohm’s law is a description used to draw conclusions about causal
19
influences and derive constraints on causal explanations of neuronal electrical activity.(*cites)
20
Like the others, it is more faithful to an idealized model than a real system. Like the others, it is
21
not used (and would not be suitable for use) as a covering law in a Deductive Nomological
22
explanation of membrane potentials, or neuronal electrical currents. Thus the equations which
23
seemed to have the best chance to qualify as laws describing Humean regularities turn out to
24
have different features and to fill different roles than Humean laws.
25
26
We saw that our explanations also involved some limited, contingent generalizations. One was
5. Another was
27
6. If the negative cross membrane voltage at one point of the membrane becomes less
28
negative until it reaches a critical threshold (of *mV in a squid axon) a nearby sodium
29
channel downstream will most probably open downstream.
30
According to SD, at least some generalizations like these should be understood, on analogy to
31
1.1 and 1.2 above as describing regularities among causal factors and their effects by virtue of
32
which certain counterfactuals of the form I  R are true where the I are ideal interventions and
33
the R are results. Thus if depolarization influences sodium channels as described, it should be
34
counterfactually the case (according to SD) that if membrane potentials are depolarized to the
35
required threshold by ideal interventions, then the probability that sodium channels open
13
We are of course ignoring a great deal, including the voltage gated potassium channels which
open to allow potassium effluxes which hyperpolarize the membrane to terminate action
02/17/16
13
1
downstream should vary in accordance with 6. And since channel openings don’t cause
2
depolarizations upstream, it should be counterfactually the case that the voltage across one bit of
3
the membrane does not change in a regular way with ideal interventions on downstream sodium
4
channels. Similarly, 5. should describe a counterfactual regularity among ideal interventions
5
which hydrolyze ATP and bindings of sodium and potassium ions. And since the average 3/2
6
sodium to potassium binding ratio does not cause ATP hydrolysis, it should be counterfactually
7
the case that ATP hydrolysis in the pump does not result from ideal interventions (if such were
8
possible) which directly bind sodium and potassium to the pump in a ratio of 3 to 2. without doing
9
anything which could independently cause ATP hydrolysis independently of the intervention.
10
5. and 6 are examples of generalizations arrived at by reasoning from the results of
11
experimental manipulations. Involving as it does the study of what happens to one item when
12
one wiggles another, the importance of this kind of research is one of the things which makes SD
13
seem plausible. But the construal of such generalizations as describing counterfactual
14
invariances involving ideal interventions is complicated by the fact that ideal interventions are not
15
always achievable in actual experimental practice. Often it is impossible or impracticable to
16
manipulate the factor of interest, and the only way to study its causal influence is by thinking
17
about what happens when experimentalists manipulate other factors they can get a handle on.14
18
Furthermore, to qualify as an ideal intervention on X with respect to Y, a manipulation must meet
19
two conditions which are often hard to satisfy. We mentioned the first requirement in connection
20
with the diphtheria toxin example. In wiggling one item to see what effect it has on another, one
21
had better not wiggle anything else that could independently produce the effect of interest. This
22
gives rise to the requirement of
23
7. Immaculate Manipulation: An intervention on X with respect to Y must change the value of
24
X in such a way that if the value of Y changes, it does so only because of the change the
25
manipulation produced in X. (Woodward *‘Explanation and Invariance in the Special
26
Sciences’ Draft 10/20/97 p.2)
27
This assumes that if X influences the values of Y, it does so as part of a system (which may
28
consist of nothing more than X and Y) which meets a modularity condition:
29
8. Modularity: The parts of the system to which X and Y belong operate independently
30
enough to allow an exogenous cause to change the values of X without producing
31
changes in other parts of the system which can influence the value of Y independently of
32
the manipulation of X.(*cite)
33
Actual experimental practice fails to satisfy these conditions in so many cases that it is more
34
natural to treat generalizations like 5. and 6. as descriptions of actual features of real world
35
systems than as counterfactual invariances involving ideal interventions. We can get an idea of
potentials.
02/17/16
1
what this amounts by comparing the generalizations to a frequentative claim about a bus route:
2
‘The #500 bus doglegs at East Liberty and returns to Highland via Penn Ave, on its way from
3
Stanton to 5th Avenue’. We can decide whether the frequentative is true by observing the bus a
4
few times, or consulting route records, and checking to make sure the route has not been
5
officially changed. We can argue for it by inferences based on regulations and practices of the
6
Pittsburgh Port Authority. We may be ingenious enough to argue for it from information about
7
what routes are available, what the road conditions are like, how fast the bus can go, and how
8
long it usually takes it to get to 5th Ave. The frequentative describes what the #500 bus typically
9
does to get from Stanton to 5th Ave. Because it is a frequentative, it can be true even if the
14
10
conditional prediction ‘If the #500 bus goes from Stanton Ave. to 5th Ave. tomorrow it will dogleg
11
at East Liberty, and return to Highland on Penn Ave.’ turns out to be false. Nor does its truth
12
depend on the truth of counterfactuals about what route the bus would have taken if it had gone
13
to 5th Ave. at times when in fact it was not running. If the frequentative is true, that is a reason to
14
expect that if the antecedent of the prediction turns out to be true, so will its consequent, but how
15
good a reason it is depends upon whether they are ever allowed to take a different route, how
16
many alternatives (if any) are available, how often emergencies make sure the standard route
17
impracticable, and so on. The frequentative also supports retrodictions about how the bus got to
18
5th Avenue in the past, but how well it supports them depends on similar factors. Unlike the
19
frequentative, the counterfactual, is not descriptive of what the bus typically does at present.
20
Unlike the prediction whose antecedent will come true if the bus goes to 5 th Ave. tomorrow,
21
nothing can happen to make its antecedent true. We discuss such counterfactuals in §n. A last
22
thing to note about the frequentative is that taken together with background knowledge that a bus
23
which crosses Penn Ave on Highland without the dogleg is likely to be jammed in traffic, it tells us
24
one thing we need to know in order to understand how the bus gets to its destination in a timely
25
fashion.
26
As the Mechanist understands them, generalizations like 5. and 6. are analogous in some
27
respects to the frequentative description of the bus route. Rather than describing counterfactual
28
regularities among ideal interventions and their results, they are partial descriptions of the modus
29
operandi of neuronal mechanisms. They support predictions and retrodictions whose truth is not
30
required for their truth. As with the description of the bus route, the reliability of predictions and
31
retrodictions based on such generalizations varies with the stability of the systems they describe
32
and the settings in which they operate. And like the description of the bus route, 5. and 6. deliver
33
information we need to understand, and to investigate further how the system they describe
34
produces effects of interest. Finally, just as the description of the bus route raises the question
35
why the route includes a dogleg, 5. and 6. set out facts which require further explanation. An
14
*examples re: 5 and 6: *(Alberts et al, p.65-6 and *cite a patch clamp depolarization
experiment)
02/17/16
15
1
adequate explanation of the resting potential would have to tell us how the Na-K pump maintains
2
the transport ration which 6 describes. An adequate explanation of the action potential would
3
have to describe the causal factors and activities which open the sodium in accordance with 6. If
4
depolarization itself influences a sodium channel how does it accomplish this, and why must it
5
reach the critical threshold in order to do so? If the channel is opened by something that causes,
6
or accompanies, or is caused by depolarization, what is it, and how does it operate?
7
iv. We do not believe SD provides a satisfactory alternative to the Mechanist account of
8
causal explanation. Before setting out our main reasons for thinking this, we note that even if
9
counterfactual invariance was as important to causality as SD takes it to be, this would not
10
11
diminish the importance of activities to causal processes and our understanding of them.
Humeanism thrives on superstitious fears about notions of causal influence which cannot be
12
reduced to regularities, and the suspicious belief that notions of actual and counterfactual
13
regularity are easier to understand or better grounded empirically. These superstitions make it
14
natural to think that as far as causality goes, there’s nothing special about activities. The idea is
15
that if regularities make the difference between causally productive and other relations, it
16
shouldn’t matter whether they involve activities. Since ideal interventions are causal processes,
17
SD cannot completely satisfy a Humean. But it promises the next best thing; the notion that X
18
exerts a causal influence need not figure in descriptions of the counterfactual invariances
19
between values of X and Y on which SD bases its account of causally productive relations
20
between the two. And even if there are some cases in which the relevant interventions would
21
bring X from inactivity to activity, counterfactual regularities involving activities should be no more
22
characteristic of causality than regularities which do not. Thus SD seems to downplay the
23
importance of activities as much as a Humean analysis. But activities are important. We don’t
24
think that actual or counterfactual regularities are essential to causality, or that all causes operate
25
with great regularity. But where regularities are to be found they tend to obtain among effects
26
and the activities which produce them.
27
28
29
30
31
32
33
34
35
36
37
38
39
40
For example ‘H. pylori causes almost all peptic ulcers, accounting for 80 percent of stomach
ulcers and more than 90 percent of duodenal ulcers.’ The bug does its work by weakening
…the protective mucous coating of the stomach and duodenum, which allows
acid to get through to the sensitive lining beneath. Both the acid and the
bacteria irritate the lining and cause a sore, or ulcer. H. pylori is able to survive
in stomach acid because it secretes enzymes that neutralize the acid. This
mechanism allows H. pylori to make its way to the "safe" area -- the protective
mucous lining. Once there, the bacterium's spiral shape helps it burrow
through the mucous lining. (http://healthlink.mcw.edu/article/956711536.html )
But
Researchers recently discovered that H. pylori infection is common in the
United States: about 20 percent of people under 40 and half of people over 60
are infected with it. Most infected people, however, do not develop ulcers.
02/17/16
16
1
2
3
4
Thus, although H pylori bugs cause ulcers as parts of a mechanism whose workings we can
5
expect to understand, ulcers do not regularly accompany H pylori infection. There is no actually
6
or counterfactually regular relation between the occurrence of ulcers and changes in the number,
7
the position, or any other features of the bacteria which are not activities. We have no reason to
8
accept counterfactual claims about what would happen to someone if a H. pylori bugs were
9
introduced into his system by a manipulation which did not make them engage in the activities
10
Why H. pylori doesn't cause ulcers in every infected person is unknown. Most
likely, infection depends on characteristics of the infected person….(ibid)
required for the production of ulcers.
11
If actual or counterfactual regularities obtain, they obtain between occurrences of ulcers and the
12
things the bacteria do to weaken and burrow through the protective mucous coating to the
13
sensitive lining beneath, the bacteria’s secretion of the enzymes which neutralize stomach acid,
14
and so on. Bacteria in different numbers and somewhat different positions may perform the same
15
burrowing and excreting activities. Depending on the condition of the digestive organ
16
environment, different activities may be carried out by H Pylori in the same spatial configurations,
17
concentrations, etc. In general the activities of the bacteria which correlate well with ulcer
18
production do not map systematically onto conditions other than activities (location of the
19
bacteria, their concentration in a given area, their movements, chemical makeup, physical
20
structure, size, and so on.) Thus it is to be expected that the regularities which obtain between
21
occurrences of ulcers and the activities of the parts of the mechanism which produces and
22
sustains them will not obtain between ulcers and values other than the ulcer producing activities
23
of the bacteria and the rest of the mechanism to which they belong. The same sorts of
24
disconnections between effects and values other than activities of their causes are typical of
25
systems which produce their effects in a regular way. Thus, even if counterfactual invariances
26
were essential to causality, the invariances would involve the activities of causal factors.
27
v. Humeans cannot account for explanations of the irregularly produced effects of unreliable
28
mechanisms. To the extent that its account of causality requires similar interventions to produce
29
similar results, SD fares no better. And some perfectly good causal explanations explain effects
30
by showing how they result from the workings of unreliable mechanisms or sub-mechanisms
31
which produce their effects irregularly and infrequently. Such systems do not exhibit the
32
counterfactual invariances SD requires. Chaotic effects illustrate this difficulty. A chaotic effect is
33
almost, if not completely, determined15 by the initial conditions of a system which is highly
34
sensitive to differences in initial conditions. The relevant differences are so small that it is
35
practically, if not theoretically impossible for investigators to discriminate among them either by
36
observation or by experimental manipulation. If the system which produces an effect is fully
By ‘almost, if not completely’, we mean there are no significant differences between values of Y
produced by the system from identical values of C.
15
02/17/16
1
chaotic, the results of its operation will be a-periodic, and observationally indistinguishable from
2
genuinely random results produced by a non-deterministic system.(*cite Lorenz)
3
17
For example, Kaplan, et al recorded trans-membrane potentials of giant squid axons to see how
4
they would change in response to periodic electrical stimulation. Each stimulus lasted 1 ms and
5
had a magnitude of .6mA. It was clear that the stimuli could (and often did) produce responses in
6
the electrical activity of the axon by raising its magnitude in comparison to a pre-established
7
threshold. Action potential spikes (AP) exceeded the threshold. Subthreshold (ST) responses
8
fell well below the threshold but were measurably above resting levels. The response patterns
9
Kaplan et al observed differed with the rate at which stimuli were administered. Regular
10
responses occurred when pulses were administered at intervals of 51ms (one AP, occurred for
11
each stimulus pulse), 26 ms (one AP occurred for every 2 pulses), 17 ms (1 AP for every three
12
pulses). Regularly occurring ST were observed for pulse intervals of 26 ms and 17 ms.
13
Presumably, the electrical pulses cause the APs. So far, this is congenial to SD. Even though
14
each of the stimulus frequencies just mentioned has its own pulse/AP ratio, it is plausible that
15
counterfactually invariant relations hold at each frequency. Regularities also obtain among
16
pulses and STs at 26ms and 17 ms frequencies. But the response patterns become irregular as
17
pulses are administered more frequently. Unevenly spaced, aperiodic APs and STs were
18
detected at intervals between 16 ms and 12. ms. And at 11.8, the STs began to occur
19
aperiodically. Kaplan et al take the irregular AP responses to be associated with ‘deterministic
20
subthreshold chaos’ which ‘can be identified as such only if the subthreshold events that occur
21
between suprathreshold activity are…analyzed.’ (Kaplan et al [1996] p. 4074 *DT Kaplan, JR
22
Clay, T Manning, L Glass, MR Guevara, A Shrier, Physical Review Letters, Vol. 76, No. 21, The
23
American Physical Society, pp.4074—4077>>. If they are right, then when stimuli are
24
administered, say every 12 ms, each AP is caused by one, or a sequence of n pulses. But it
25
need not be the case that the next pulse, or the next n pulses will produce an AP. And there will
26
be no way to evaluate counterfactual claims about what would have happened if an axon had
27
been stimulated at a slightly different time than it was. We don’t think this means the observably
28
or experimentally discriminable electrical pulses exerted no causal influence on the production of
29
APs or STs. If the system is chaotic, invariant relations might hold between APs and STs and
30
quantities which cannot be distinguished from one another by actual (non-ideal) measurements
31
or experimental manipulations. But these quantities are not to be confused with the pulses which
32
can be experimentally controlled and distinguished from one another. The latter cause ST and
33
AP responses, but do not produce them in anything like a regular way when they are
34
administered every 12 ms.
35
vi. A counterfactual conditional is true whenever things are such that if its antecedent were
36
true, had been true in the past, or will be true in the future, so would its consequent. It is false
37
whenever things are such that if the antecedent were (had been, will be) true, its consequent
02/17/16
18
1
would be (would have been, will be) false. Whenever there is no fact of the matter as to what
2
would happen (would have happened, will happen) if the antecedent were (had been, will be)
3
true, the counterfactual has no truth value. For example, suppose that now, at t1, you predict that
9. if it there is a sea battle at t2 (at some specified time after t1) then the officers’ ball
4
5
scheduled that day will be cancelled.
6
The antecedent of 9. is not true whenever things are such that that there will be no sea battle t2,
7
or things are up in the air with regard to whether there will be. We will say that 9. is unrealized at
8
every such time, and similarly for all other counterfactuals. Some conditionals which are
9
unrealized at one time become realized at another. If the sea battle occurs at t2 9. is realized at t2
10
and every subsequent time. If something happens at any time before t 2 to make the sea battle
11
inevitable, 9. is realized from that time on.16 If there is no sea battle at t2, 9. is never realized.
12
Some conditionals are not only unrealized, but unrealizable. The counterfactual conditional ‘if 2
13
were greater than 4, then 2 would be greater than 3’ is an example. Some conditionals are never
14
realized even though there are times at which they could have been. Thus even though
15
something could have happened during the 1948 election to make its antecedent true, the
16
counterfactual conditional, ‘(Harry Truman lost the 1948 election)  (Harry Truman is not
17
President in 1949)’ turns out never to be realized. Some never to be realized conditionals have
18
truth values by virtue of logical, mathematical, and other principles (taken together, in some cases
19
with matters of contingent fact). ‘(pi = 3.7)  (circles have bigger areas than they’ve been
20
telling you)’ is an example.
21
SD must assume that never to be realized counterfactual conditionals about interventions and
22
their results have truth values. This assumption is problematical. It counts in favor of Mechanism
23
that it need not assume it. Recall that according to Woodward, if one item, X, exerts a causal
24
influence on another, Y, then
25
10. Invariance: the values of Y vary in a regular way with at least some ideal interventions
26
consisting of manipulations of the value of X,
27
The interventions must be performed on systems which satisfy the Modularity requirement (8),
28
and must qualify as Immaculate (7.) to ensure that if the value of Y changes, the change will be
29
due exclusively to the change the intervention makes in the value of X.
30
Interventions meeting these conditions are commonly represented by assigning values to
31
variables in directed acyclic graphs (DAGs) which meet Judea Pearl’s, Peter Spirtes’, Clark
32
Glymour’s, and Richard Scheiness’ conditions for causal Bayesian networks.(*cite Causality pp
33
23—24, SGS…). Ignoring details,17 these graphs consist of nodes connected by lines and arrows
16
*Anscombe on the sea battle.
One such detail, extremely important in other contexts, is that the algorithms used to construct
DAGs from statistical data obtained from a real system often deliver, not a single DAG, but a
class of different graphs, each of which represents a somewhat different causal set up capable of
17
02/17/16
19
1
arranged to represent probabilistic relations between factors belonging to real causal systems.
2
Each node is a variable representing a different part of the causal system of interest. The arrows
3
represent probabilistic relations among values of variables such that the variable at the tail of an
4
arrow screens off the variable at its point. The construction and use of a DAG are constrained by
5
probabilistic relations of independence and dependence between various factors exhibited by the
6
data from the system of interest. They are also constrained by various assumptions about that
7
system18. They employ algorithms which determine, among other things, what if any impact the
8
assignment of a new value to one of the variables in the graph would have on the assignments of
9
values to other variables in the graph. And there are theorems to determine the scope and limits
10
of the algorithms. If variables X and Y represent parts X and Y of a real system, an ideal
11
intervention on X with respect to Y is represented by assigning a new value to X without changing
12
the value of any variables except those at the heads of arrows leading back to X.19. When a new
13
value is assigned to X, the algorithms, etc., are used to determine .(—in conformity with the
14
probability distributions over the data) what changes (if any) to make in the assignments of values
15
to Y and any nodes connected by arrows running between them.
16
But nodes in graphs are not to be confused with the parts of the systems they represent.
17
Furthermore DAGs typically represent simplified and idealized version of the real system to
18
which X and Y actually belong. If there are non-negligible discrepancies between the real and the
19
idealized or simplified system, we can’t conclude straightway from a graph just what would
20
happen in the real system if X were actually manipulated. Thus the fact that Y must be assigned
21
a value of such and such if X is assigned a value of so and so need not be sufficient to determine
22
the truth value of a prediction about what will result from an actual manipulation. This is most
23
obvious where the real system fails to meet one or more of the conditions (see n. 18) assumed to
producing data which are the same in all relevant respects.(Spirtes & Scheiness in McKim and
Turner, p.166)
18 For example, the Markov Rule, requires the graph to be so constructed that if n is the variable
i
at the tail of an arrow, and nj is the variable at its head, ni must screen off nj from every node at
the tail of an arrow leading to ni. If one or more other nodes, nk are at the tails of arrows with ni at
their heads, ni must screen nj off from the nk. And so on. An important general assumption is that
the system of interest produces data in such a way that the probabilistic independencies among
its members follow from Markov condition applied to a DAG which represents it so that, e.g., if the
graph includes an arrow with X at its head and Y at its tail, variables, X and Y, the counterparts
of these variables in the data obtained from the system of interest are neither independent nor
conditionally independent on one another.(Glymour in McKim p.209) A system which meets this
condition is said to be faithful to a DAG which represents it. To assume that a system is faithful is
to assume that ‘whatever independencies occur [in the relevant population] arise not from some
incredible coincidence, but rather from [causal] structure.(Scheiness in McKim p.194). It may (but
is not always) assumed that the values of the variables included in the graph do not have any
common causes which are not represented in the graph.(Glymour in McKim p.217)
19 An arrow leads back to X if it has X at its tail. Or if the variable at its head is at the tail of
another arrow at its head. And so on.
02/17/16
20
1
hold in constructing and using the DAG. 20 Furthermore, we will argue that if ‘I  R’ is a never to
2
be realized counterfactual which claims that the value of a real item, Y, would change as
3
described by R if an ideal intervention, I, were performed on a real item ,X, it does not follow from
4
the fact that we can tell what value to assign to Y in a DAG that there is any answer to the
5
question whether ‘I  R’ is true or false.
6
Some effects are caused by, and must be explained in terms of, factors which humans lack the
7
strength, the understanding, the resources or the willingness, moral courage, or moral
8
callousness to manipulate. Accordingly Woodward understands ideal interventions non-
9
anthropomorphically without essential reference to notions like human agency.(*p.6). When
10
humans cannot or will not intervene in natural systems, nature may do the job for them. But in
11
some systems, the factors involved in the production of the effect to be explained are so
12
entangled that (8) the Modularity requirement is violated and immaculate manipulations cannot be
13
accomplished. For example (attributed by Woodward and Hausman to Eliot Sober) consider
14
15
16
17
18
19
20
21
the claim that the gravitational force exerted by one massive body causes
some effect (such as tides) on a second. It is possible that any physically
possible process that would change the force exerted by the first on the
second (by changing the position of the first) would require a change in the
position of some third body and this would in turn exert a direct effect on the
second in violation of one of the conditions for intervention. (Woodward and
Hausman ([1999] n 12, p.537)
22
The nervous system is one of many biological systems which provide further examples. 21 In at
23
least some of these cases causal factors can be identified, and the results of their influences
24
ascertained even though ideal interventions cannot occur, and counterfactuals whose
25
antecedents describe them are never realized.
26
Nuel Belnap has argued that predictions about the results of non-deterministic causal
27
processes have no truth values until what they predict either happens or fails to happen.(*cite)
28
We believe that similar arguments can be applied to counterfactual conditionals to show that
29
never to be realized counterfactual conditionals about non-deterministic systems have no truth
30
values. If this is correct, only deterministic systems can satisfy the Invariance condition (10).
20
It is worth noting that Glymour, Spirtes, Scheiness emphatically do not believe that real
systems meet all of the conditions they elaborate. Indeed, they conceive their project as
determining what can be learned from statistical data about systems which meet all of them, what
if anything can be learned when one or more of their conditions are not met, and what, if
anything, can be done to decide whether a given condition is satisfied by the system which
produced the data of interest.(Glymour in McKim, p.210, 217)
21 One of them is the human nigrostriatal system which regulates motor outputs through an
elaborate arrangement of strongly interconnected inhibitory and excitatory feedback
mechanisms.(*Cite Black pp.68ff. *Ira B Black, Information in the Brain, Cambridge, MIT, 1994).
Another is the sea snail sensitization mechanism by which neurotransmitter molecules operating
in a presynaptic terminal initiate postsynaptic activity in response to a stimulus, while changing
the structures their influence depends upon in such a way that continued stimulation produces
02/17/16
21
1
It is to Mechanism’s credit that it does not appeal to counterfactual regularities in a way which
2
limits its application to deterministic systems.
3
Where t0, is an interval of past time just big enough for the occurrence of an immaculate
4
intervention, I, on X, t1 is a later interval just big enough for R, a specified change in the value of
5
Y, and t2 is any interval of time of any size after t1, consider the claim
6
11. It is the case at t2 that I at t0 R at t1,.
7
Whether or not the intervention could have occurred at t0, 11. if it did not occur, 11. is unrealized
8
at all times because nothing which happens after t0 to change the past as required to bring it
9
about that the intervention did occur then. To see why 11. has no truth value if X and Y belong to
10
a non-deterministic system, consider Fig 1, a diagram we adapted from Nuel Belnap’s and
11
Mitchell Green’s treatment of predictions.22
12
Fig. 1
13
14
The parallel lines in this diagram are time lines representing intervals t o, t1, t2, and so on. Let a
15
moment be everything that is actually going on at every place during any single temporal
increasingly less postsynaptic activity.(Black pp.30-31) Still others are to be found in sensory
processing carried out by larger neuronal structures.(*ex: and cite)
22 *cite, disclaim, etc.
02/17/16
22
1
interval.23 Each interval up to and including the present contains exactly one actual moment. For
2
the actual moment whose members are actually going on during any given interval, t i, there are
3
any number of mutually incompatible moments, each one of which includes one or more things
4
which could be, but are not going on during ti. A non-actual, possible moment may contain one or
5
more actual happenings, but at least one of its components must be merely possible; only actual
6
moments contain exclusively actual components. A history is
…a maximal chain of moments, a complete possible course of [causally
related] events stretching all the way back [into the past] and all the way
forward [beyond the present].(Thin Red Line, p.139) 24
7
8
9
10
In our diagram, histories are represented by ascending lines. A segment of a history (actual or
11
possible) is a part consisting of one or more connected moments. Ha is a segment of the history
12
whose moments are all actual up to the present (t2). It’s components include actual moments
13
from t2, t1, t0, and before. Assuming non-determinism, we can suppose that a number of possible
14
segments (perhaps infinitely many) branch off of HA before t2 in addition to the segment whose
15
moments turned out to be actual. The non-bold lines branching from Ha before t2 indicate a very
16
few of them.. Even if one of these segments contained more highly probable happenings than
17
the others, there is not at t2 a fact of the matter as to which possible continuation will be actual. A
18
number of possible, but non actual history segments which branch off of HA at t0. A number of
19
others, like H9, extend from t0 back into the past, but do not do not share any moments with HA.
20
Some possible but non-actual history segments (e.g., H7, H8 ) include I at t0 and R at t1 relative to
21
these, 11. is true and SD can consider X to be causally productive of R. In others, (e.g., H5, H6) I
22
occurs at t0 and R does not occur at t1. Relative to these 11. is false, and according to SD, X is
23
not causally productive of R. But there is no fact of the matter at t2 whether, if I had actually
24
occurred at t1 it would have belonged to a segment in which R occurred at t1. Unless there is
25
some reason why 11. should be true by virtue of possibilities like H7 and H8, instead of false by
26
virtue of possibilities like H5 and H6, 11 has no truth value. We submit there is not, and that any
27
choice of an I at t0 with which to assign a truth value would be arbitrary. 25 , 26
28
This might not seem to be an unwelcome result for SD. Why not understand non-deterministic
29
causal influences in terms of probabilistic invariances? We suppose this would involve never to
30
be realized counterfactuals according to which the probabilities of effects involving specific
31
changes in the values of Y vary in a regular way with at least some ideal interventions on a
32
causal influence, X. As we understand it, probabilistic invariances would depend upon the truth
33
of claims of the form P(R at t1 |I at t0) =n which assign a value of n to the probability of R at t1
23
* Moments are thus the ontological counterparts of state descriptions.
Whose moments, unlike ours, are vanishingly small.
25 *note on Lewis and measures of closeness
26 Relative to histories which do not contain I at t , 6. will be vacuously true by virtue of the falsity
0
of its antecedent, but so will ‘I at t0  R at t1.
24
02/17/16
23
1
conditional on I at t0.27 It is hard to see how such claims can have truth values. Let S 1, S2……be
2
different segments of possible histories. Let each segment extend back from t 0 to some time
3
before t0, and let each segment include I at t0. A number of different possible continuations will
4
branch off of each of the Si at t0. Some of the continuations of any given segment will include R
5
at t1, but others will not. Neither we nor Woodward believe that the obtaining or non-obtaining of
6
causally productive relations depends upon assignments of subjective probability. Thus if X
7
exerts a causal influence on the probability of Y’s assuming some value, the probability of R at t1
8
conditional on I at t0 must be an objective probability whose values do not depend upon any real
9
or ideal agent’s betting habits, strengths of the beliefs, etc. The only way we can understand
10
values of n as measurements of objective, rather than subjective probabilities of R at t1
11
conditional on I at t0 is to think of them as functions of how many continuations of segments
12
including I at t0 do, and how many do not include R at t1. We might suppose, for example, that if
13
S1 is a segment with I at t0, and R at t1 in one third of its continuations, then P(R at t1 |I at t0 =
14
.333 relative to S1. If S2 is a segment with I at t0 and R at t1 in half of its continuations, then P(R
15
at t1 |I at t0 = .5 relative to S2. And so on. See Fig. 2 below. It may happen that different
16
segments with I at t0 branch off into continuations with different proportions of occurrences to non
17
occurrences of R at t1. Then P(R at t1 |I at t0) will have different values relative to different
18
segments of these possible histories. Thus some segments which contain I at t0 will have
19
continuations which satisfy a counterfactual claim about how the probability of R at t1 is related to
20
I at t0 and others will not.
21
counterfactuals about ideal interventions and their results have truth values faces the same
22
difficulties as the supposition that non-probabilistic counterfactuals like ‘I at t0  R at t1’ have
23
truth values. Someone might suggest that the probability of R at t1 conditional on I at t0 is a
24
function of the total number of possible histories including both the intervention and the result and
25
the total number of possible histories which include the intervention, without the result. But if this
26
assumes that all of the I at t0 histories should be equally weighted in calculating P(R at t1|I at t0),
27
we see no reason for weighting them this way. And if it assumes weighting different histories
28
differently, we know of no principled way to assign the weights
27
As long as this is possible, the supposition that unrealized
In addition, if changes in the values of Y are not to exert a causal influence on ideal
interventions on X, certain claims about the probabilities of the latter conditional on the former will
have to be false. Although we will not discuss this, it raises the same kinds of difficulties as the
claims we do discuss.
02/17/16
1
24
.
2
Fig. 2.
3
4
Suppose things have transpired in the actual history of the world at some time, t -1, before t0 to
5
make the I impossible at t0 because the system X and Y belong to did not evolve in a form which
6
satisfies the Modularity condition (8.) or because no causes available at t0 can immaculately
7
manipulate X with respect to Y. Then I can and does occur at t0 only in segments in which the
8
system to which X and Y belong, or the environment in which that system functions, differs
9
significantly from their counterparts in HA. This complicates the assignment of probabilities
10
considerably. Furthermore if we want to know whether X exerts a causal influence on the
11
probabilities of specified values of Y, what we’re interested in is what X actually did, actually
12
does, or will actually do to Y. Many of the segments of possible histories in which I occurs at t0
13
will be too exotic for us to learn much about that from how many of their continuations do, and
14
how many do not contain R at t1.
15
vii. Recall Sober’s example in which a tidal effect was explained as due to a factor which
16
could not be immaculately manipulated. Woodward and Hausman responded that despite its
17
impossibility, the laws of physics might determine what the ideal intervention could accomplish.
18
(*Cite) As this suggests, SD’s best hope for truth values for never to be realized counterfactuals
19
might be to embrace determinism and assume that for every good causal explanation, there are
20
laws available to decide what would have happened if the relevant ideal intervention had been
21
accomplished. But then SD collapses into a form of Humeanism according to which there are
22
laws to determine not just how the actual history of the world will continue into the future, as well
23
as the developments of alternative possible histories. This is not a happy option. A main reason
24
for wanting an alternative to Humeanism was that at least with regard to biology and other special
25
sciences there are good empirical reasons to doubt whether such laws are can be found in
02/17/16
1
connection with every good causal explanation. Furthermore, to the extent that it assumes the
2
existence of laws to evaluate never to be realized counterfactuals, SD burdens itself with long
3
standing, vexed questions about how we can tell which generalizations are true, exceptionless
4
and blessed with the modal status and the other virtues of genuine laws. It is to Mechanism’s
5
credit that although it raises epistemological questions, these are not among them.
6
25
DAGs can sometimes be used without invoking Humean laws to evaluate never to be realized
7
counterfactuals about the results of ideal interventions. The most favorable cases for their use
8
are those in which the distribution of observed quantities in a body of data satisfies all of the
9
conditions (see n.18) required for the construction of an optimal representation of a causal
10
system. When this happens, calculations of how the value of one variable in a DAG are to be
11
adjusted when new values are assigned to another can be sufficient to determine truth value of a
12
never to be realized counterfactual about an ideal intervention on the system the DAG
13
represents—even if the intervention requires a manipulation which neither man nor nature can
14
achieve.(But see n.17). But Glymour, Spirtes, and Scheiness and are the first to admit that many
15
bodies of data fail to meet one or more of their conditions. 28 This places limitations on how much
16
a DAG can tell us. How serious they are depends on which conditions are unsatisfied, and which
17
ideal interventions are of interest. We assume that at least some troublesome bodies of data
18
arise from systems which produce effects whose causes we nevertheless can understand quite
19
well. Thus if SD relied on the ability of DAG techniques to establish the truth values of never to
20
be realized counterfactuals about ideal interventions on real systems, it would incur the same
21
epistemological burdens which non-ideal bodies of data place upon Glymour, Spirtes, and
22
Scheiness. It is to Mechanisms advantage that these are not its burdens.29 .
23
The most pressing epistemological questions raised by Mechanism are the following.
24
a] How do we know what activities the parts of a mechanism engages in? For example, how
25
we can know that the Na-K pump transports sodium out of the neuron and potassium in, or that
26
sodium channels open and close or that H pylori weakens the mucous coating which protects the
27
stomach lining, or that it burrows into the lining, and excretes an acid neutralizing substance?
28
b] How do we find out about the manner in which the relevant activities are carried out? For
29
example, how do we know that on average the Na-K pump removes 3 Na ions for every 2 K ions
28
For example, there are limits to what their methods can accomplish in some cases where
DAGs must be constructed from data generated in part by unmeasured causes, even though
there are other such cases in which the counterfactuals about interventions can be evaluated
(CPS pp.170ff., Glymour in McKim pp.242, Scheiness in McKim pp.197—99).
29 *Note: CPS methods may often be employed (e.g., in experimental design) to investigate
questions Mechanism believes must be answered in order to find the causes of real world
phenomena. Accordingly, it grants the epistemic importance of solving the problems raised for
CPS by imperfect data. In saying these are not its problems, we mean that because the
Mechanist account of causal relations does not assume that the truth values of never to be
realized counterfactuals can be ascertained, its acceptability does not depend upon answers to
questions about how much CPS can do when it is applied to non-optimal data.
02/17/16
26
1
it admits into the cell, and that it accomplishes this in part through changes in its configurations?
2
This, like a], is a special case of the question how we know whether a frequentative is true.
3
c] How do we know what contributions the activities of a part make to the production of the
4
effect of interest? For example, how do we know that the Na-K pump helps maintain the resting
5
potential by admitting and expelling positively charged ions to compensate for small
6
depolarizations due to leakage; that by opening, the sodium channel admits enough positively
7
charged ions into the cell to produce or maintain an intracellular current at a fixed magnitude; that
8
the bug’s weakening of the mucous coating contributes to the production of an ulcer by allowing
9
digestive acid to reach membrane to irritate it; and that by exuding an acid neutralizing
10
11
substance, the bug keeps the acid from destroying it before it can complete its work?
Although this is not the place to try to answer these questions (and although we do not have
12
complete answers to them), we submit that they are by no means as difficult as the
13
epistemological questions about the evaluation of never to be realized counterfactuals which SD
14
raises.
15